Micromagnetic simulation in which a magnetic substance is modeled as an assembly of small magnets and the domain state is numerically simulated is known as a technology for analyzing the magnetization behavior of a magnetic substance. Micromagnetic simulation is used to analyze the domain state of a micromagnetic device, such as a magnetic head of a hard disk drive (HDD) or a magnetoresistive random access memory (MRAM), and a magnetic material, such as a permanent magnet or a magnetic steel sheet.
FIG. 13 is a diagram for explaining modeling of a magnetic substance by micromagnetization. The micromagnetization refers to individual small magnets. As illustrated in FIG. 13, a magnetic vector 92 is calculated per micromagnetization 91 in micromagnetic simulation.
In micromagnetic simulation, in order to ensure the calculation accuracy, the mesh size is adjusted such that the angles formed by magnetization vectors of meshes adjacent to each other are small angles so that the magnetization directions are regarded as approximately continuous. The mesh size is requested to be smaller than an exchange length. Particularly, in domain analysis on a permanent magnet with great magnetic anisotropy, the exchange length decreases to approximately one nanometer (nm). The exchange length represents the diameter of a crystal grain where an exchange occurs.
When calculations are performed according to the tissue structure of a permanent magnet, because the permanent magnet has a crystal grain size of few micrometers (μm), the number of meshes increases with a mesh size of approximately 1 nm. If the mesh size is increased, flexibility used for calculations lowers, which can shorten the calculation time; however, because the angles formed by magnetization vectors adjacent to each other increase, the calculation accuracy significantly worsens. For this reason, if the mesh size is increased without consideration, the calculation accuracy is not ensured.
Thus, there is a related technology in which the angle of rotation between two magnetization vectors arranged at the centers of elements (meshes) adjacent to each other is interpolated with reference to the rotation axis perpendicular to the two magnetization vectors and an exchange field is calculated.
There is another related technology in which an effective magnetic field that acts on each element to be analyzed is calculated using, as a fixed value, a magnetic field calculated by magnetic field analysis using a finite element method and a magnetization vector in each element is calculated using the calculated effective magnetic field, so that the speed of analyzing the characteristics of a magnetic substance is increased.
There is still another related technology in which a magnetic substance is divided into an analysis region and a non-analysis region and the non-analysis region is coarse grained using a representative region, so that the time for calculating the demagnetizing field from the non-analysis region acting on the magnetization in the analysis region and the calculation resources are reduced.
Patent Document 1: Japanese Laid-open Patent Publication No. 2012-033116
Patent Document 2: Japanese Laid-open Patent Publication No. 2013-131072
Patent Document 3: Japanese Laid-open Patent Publication No. 2013-196462
Micromagnetic simulation has a problem in that an increase in the mesh size worsens the calculation accuracy. For this reason, a technology that allows accurate simulations even with a mesh size that worsens the calculation accuracy is important.